Question

find the sum of all even numbers between 100 and 200​

Answer 1

Answer:

We’re adding up all of the even numbers from 100 to 200. There are 100 numbers from 101 to 200, which means there are 50 even numbers. Since 100 is also included in our sum, we’re adding 51 even numbers all together.

Let’s reorder the numbers:

100+102+104+…+198+200

=(100+200)+(102+198)+(104+196)+…+(148+152)+150

If we look at the reordered sum, we can see that there are 25 pairs of even numbers plus an extra 150. Each pair sums to 300, so the total is

=25x300+150

=7500+150

=7650.

Answer 2

50

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